Q19 of 47 Page 1

A solid metallic sphere of diameter 16 cm is melted and recasted into smaller solid cones, each of radius 4 cm and height 8 cm. Find the number of cones so formed.

Given:

Diameter of sphere = 16 cm


∴ Radius of sphere, r = 8 cm


Radius of cone, R = 4 cm


Height of cone, H = 8 cm


Let a solid sphere be melted and recasted into n smaller solid cones.


So, volume of sphere = n (Volume of cones)


We know that volume of sphere = (4πr3)/3


And Volume of cone = πr2h/3


∴ (4πr3)/3 = n (πR2H/3)


⇒ (4π (8)3) / 3 = n (π (4)2 (8)) / 3


⇒ (4 (512)) = n (128)


⇒ 2048 = n (128)


⇒ n = 2048 / 128


∴ n = 16


Ans. Number of cones made by melting a given solid sphere is 16.


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